Abstract:
A higher-order approximation analytical solution for a current-carrying ion sheath is automatically derived in computer by decomposition method. Chaos behaviors in the system driven by an external periodic oscillation are controlled using feedback control strategy. Its effectiveness is verified by numerical simulations.

Abstract:
This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.

Abstract:
A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security.

Abstract:
Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying the onset of an inherent bifurcation, stabilizing a bifurcated solution or branch, changing the parameter value of an existing bifurcation point, modifying the shape or type of a bifurcation chain,introducing a new bifurcation at a preferable parameter value, monitoring the multiplicity, amplitude, and/or frequency of some limit cycles emerging from bifurcation, optimizing the system performance near a bifurcation point, or a combination of some of these objectives. This article offers an overview of this emerging, challenging, stimulating, and yet promising field of research,putting the main subject of bifurcation control into perspective.

Abstract:
The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.

Abstract:
In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.

Abstract:
Fuzzy logic control (FLC) based on tracking error feedback is called conventional FLC in this paper. A thorough study of the conventional FLC on its dual features is presented. Both linguistic and numerical analyses show that conventional FLC combines properties of its linear control and variable structure control (VSC) components. These features can be adjusted by tuning the scaling gains and membership functions (MFs). Using large gains or more MFs result in stronger VSC effect but less linear control effect, and vice versa. Simulation results have confirmed this analysis. As VSC is usually advantageous for complex processes while linear control is better for simpler ones, the influence of these dual features on FLC design and tuning is significant. Thus, initial gains of FLC are suggested to be designed based on the well-tuned linear control structure for a simple process, and they can be determined based on the VSC theory for a complex process. These dual features can also help understand the robustness of the conventional FLC systems.

Abstract:
In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.

Abstract:
Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster coupling condition is not always needed for the diffusively coupled network. Several sufficient conditions are obtained by using the Schur unitary triangularization theorem, which extends previous results. Some numerical examples are presented for illustration.

Abstract:
A simple three-dimensional (3D) autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll, 2-scroll and 4-scroll attractors, as well as hyperchaotic attractors, by simply tuning a single system parameter. Lyapunov exponents and bifurcation diagrams are obtained via numerical simulations to further justify the existences of chaos and hyperchaos. Finally, an electronic circuit is constructed to implement the system, with experimental and simulation results presented and compared for demonstration and verification.